The tips at the ends of shoelaces are generally made by wrapping the ends with metal or with thermoplastic which can be made rigid. It is one purpose of this invention to make rigid tips at the ends of shoelaces without the addition of tipping material by rigidifying the material of the lace itself, thus effecting a substantial economy in the manufacture of the laces. The method embodies reducing the cross section of the lace at the end portions and welding the fibers or filaments of the constituent yarns of the lace to each other and, hence, it has application in addition to forming tips at the ends of shoelaces comprised of a concatentation of yarns to the welding of two or more yarns to each other at predetermined intervals to form multistrand structures or to the welding of adjacent or crossing portions of yarns arranged in predetermined relation to form a dimensionally stable structure.